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## Johnson, Charles Royal

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 Author ID: johnson.charles-royal Published as: Johnson, Charles R.; Johnson, C. R.; Johnson, Charles; Johnson, Ch. R.; Johnson, C. Homepage: https://www.wm.edu/as/mathematics/faculty-directory/johnson_c.php External Links: MGP · Wikidata · dblp · GND · IdRef
 Documents Indexed: 465 Publications since 1970, including 15 Books
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#### Co-Authors

 52 single-authored 21 Olesky, D. Dale 20 van den Driessche, Pauline 19 Saiago, Carlos M. 18 Fallat, Shaun M. 16 Furtado, Susana 16 Smith, Ronald L. 15 Leal-Duarte, António 13 Barrett, Wayne W. 12 Marijuán, Carlos 12 Pisonero, Miriam 11 Lundquist, Michael E. 10 Drew, John H. 10 Spitkovsky, Ilya Matvey 9 Horn, Roger Alan 9 Kroschel, Brenda K. 9 Loewy, Raphael 9 Nylen, Peter M. 8 Farber, Miriam 8 Reams, Robert B. 8 Stanford, David P. 8 Toyonaga, Kenji 8 Zhang, Yulin 7 Pierce, Stephen J. 7 Rodman, Leiba X. 7 Tarazaga, Pablo A. 7 Wolkowicz, Henry 6 Elsner, Ludwig F. 6 Hillar, Christopher J. 6 Paparella, Pietro 5 Bakonyi, Mihály 5 Carlson, David Hilding 5 Eschenbach, Carolyn A. 5 Howe, Eric C. 5 Lins, Brian 5 Narayan, Sivaram K. 5 Newman, Morris 5 Sutton, Brian D. 5 Szulc, Tomasz 5 Tsatsomeros, Michael J. 4 Dopico, Froilán M. 4 Gekhtman, Michael I. 4 Li, Chi-Kwong 4 Markham, Thomas L. 4 Marques de Sá, Eduardo 4 Maybee, John S. 4 Nasserasr, Shahla 4 Neumann, Michael 4 Peña, Juan Manuel 4 Schreiner, Erik A. 4 Turnansky, Morrison 4 Walch, Olivia 3 Bru, Rafael 3 Charles, Zachary B. 3 Dorsey, Jonathan 3 Graves-Morris, Peter R. 3 Grone, Robert D. 3 Hauke, Jan 3 Hershkowitz, Daniel 3 Kellogg, Bruce 3 Kennedy-Shaffer, Lee 3 McMichael, Paul R. 3 Perdigão Dias da Silva, José António 2 Barnett, Stephen 2 Booth, Matthew 2 Costas-Santos, Roberto S. 2 DeAlba, Luz Maria 2 Faulk, Mitchell 2 Fiedler, Miroslav 2 Gannon, Tom 2 Gelonch, José 2 Hackney, Philip 2 Hall, Frank J. 2 Harris, Benjamin 2 Hogben, Leslie 2 Jankowski, Eric 2 Kirk, Ryan 2 Laffey, Thomas J. 2 Lay, David Clark 2 Lay, Margaret 2 Leighton, Frank Thomson 2 Lenker, Terry D. 2 Lewis, Drew 2 Link, Joshua A. 2 Marzion, Evan 2 Mitchell, Lon Howard 2 Nævdal, Geir 2 Nath Datta, Biswa 2 Okubo, Kazuyoshi 2 Pascoe Streib, Amanda 2 Plemmons, Robert James 2 Porter, A. Duane 2 Robinson, Herbert A. 2 Shalom, Tamir 2 Sher, David A. 2 Šmigoc, Helena 2 Sokal, Alan D. 2 Soto, Ricardo Lorenzo 2 Stephens, Arthur B. 2 Wakhare, Tanay V. 2 Wei, Zhen ...and 160 more Co-Authors
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#### Serials

 170 Linear Algebra and its Applications 87 Linear and Multilinear Algebra 25 SIAM Journal on Matrix Analysis and Applications 20 ELA. The Electronic Journal of Linear Algebra 13 Journal of Research of the National Bureau of Standards 12 Discrete Mathematics 8 Proceedings of the American Mathematical Society 7 SIAM Journal on Algebraic and Discrete Methods 5 Special Matrices 4 American Mathematical Monthly 4 Discrete Applied Mathematics 4 Journal of Mathematical Analysis and Applications 4 Czechoslovak Mathematical Journal 3 Positivity 3 Involve 3 Asian-European Journal of Mathematics 2 Journal of Research of the National Bureau of Standards 2 Rocky Mountain Journal of Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Computational Optimization and Applications 2 Numerical Linear Algebra with Applications 2 Mathematical Inequalities & Applications 2 Cambridge Tracts in Mathematics 2 MAA Notes 1 International Journal of Control 1 Journal of Statistical Physics 1 Mathematics of Computation 1 The Arabian Journal for Science and Engineering 1 Automatica 1 Canadian Mathematical Bulletin 1 Journal of Approximation Theory 1 Journal of Combinatorial Theory. Series B 1 Journal of Functional Analysis 1 Journal of Mathematical Economics 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Networks 1 Pacific Journal of Mathematics 1 Portugaliae Mathematica 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Advances in Applied Mathematics 1 Circuits, Systems, and Signal Processing 1 Journal of Theoretical Probability 1 SIAM Journal on Discrete Mathematics 1 Aequationes Mathematicae 1 Economic Theory 1 The Electronic Journal of Combinatorics 1 Reliable Computing 1 Taiwanese Journal of Mathematics 1 Mathematical Proceedings of the Royal Irish Academy 1 Discussiones Mathematicae. General Algebra and Applications 1 Portugaliae Mathematica. Nova Série 1 Proyecciones 1 Contemporary Mathematics 1 Proceedings of Symposia in Applied Mathematics 1 Operators and Matrices 1 The College Mathematics Journal 1 Discrete Mathematics, Algorithms and Applications 1 Princeton Series in Applied Mathematics
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#### Fields

 418 Linear and multilinear algebra; matrix theory (15-XX) 127 Combinatorics (05-XX) 35 Numerical analysis (65-XX) 19 Operator theory (47-XX) 19 Systems theory; control (93-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Group theory and generalizations (20-XX) 6 Operations research, mathematical programming (90-XX) 5 General and overarching topics; collections (00-XX) 5 Number theory (11-XX) 5 Real functions (26-XX) 5 Probability theory and stochastic processes (60-XX) 5 Computer science (68-XX) 4 History and biography (01-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Commutative algebra (13-XX) 4 Geometry (51-XX) 4 Convex and discrete geometry (52-XX) 4 Statistics (62-XX) 3 Mathematical logic and foundations (03-XX) 3 Ordinary differential equations (34-XX) 2 Functions of a complex variable (30-XX) 2 Integral transforms, operational calculus (44-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

368 Publications have been cited 10,358 times in 8,234 Documents Cited by Year
Matrix analysis. Zbl 0576.15001
Horn, Roger A.; Johnson, Charles R.
1985
Topics in matrix analysis. Zbl 0729.15001
Horn, Roger A.; Johnson, Charles R.
1991
Matrix analysis. Reprinted with corrections. Zbl 0704.15002
Horn, Roger A.; Johnson, Charles R.
1990
Matrix analysis. 2nd ed. Zbl 1267.15001
Horn, Roger A.; Johnson, Charles R.
2013
Topics in matrix analysis. 1st paperback ed. with corrections. 1st pbk with corr. Zbl 0801.15001
Horn, Roger A.; Johnson, Charles R.
1994
Positive definite completions of partial Hermitian matrices. Zbl 0547.15011
Grone, Robert; Johnson, Charles R.; Marques de Sá, Eduardo; Wolkowicz, Henry
1984
Totally nonnegative matrices. Zbl 1390.15001
Fallat, Shaun M.; Johnson, Charles R.
2011
Row stochastic matrices similar to doubly stochastic matrices. Zbl 0455.15019
Johnson, Charles R.
1981
Inverse M-matrices. Zbl 0488.15011
Johnson, Charles R.
1982
The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree. Zbl 0929.15005
Johnson, C. R.; Duarte, António Leal
1999
The Parter–Wiener theorem: Refinement and generalization. Zbl 1067.15003
Johnson, Charles R.; Duarte, António Leal; Saiago, Carlos M.
2003
Normal matrices. Zbl 0613.15021
Grone, Robert; Johnson, Charles R.; Marques de Sá, Eduardo; Wolkowicz, Henry
1987
Numerical determination of the field of values of a general complex matrix. Zbl 0389.65018
Johnson, Charles R.
1978
Spectrally arbitrary patterns. Zbl 0957.15012
Drew, J. H.; Johnson, C. R.; Olesky, D. D.; van den Driessche, P.
2000
Hermitian matrices, eigenvalue multiplicities, and eigenvector components. Zbl 1083.15015
Johnson, Charles R.; Sutton, Brian D.
2004
The real and the symmetric nonnegative inverse eigenvalue problems are different. Zbl 0861.15007
Johnson, Charles R.; Laffey, Thomas J.; Loewy, Raphael
1996
The Perron root of a weighted geometric mean of nonnegative matrices. Zbl 0684.15007
Elsner, L.; Johnson, Charles R.; Dias da Silva, J. A.
1988
Completely positive matrices associated with $$M$$-matrices. Zbl 0815.15019
Drew, John H.; Johnson, Charles R.; Loewy, Raphael
1994
On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree. Zbl 1002.15010
Leal-Duarte, António; Johnson, Charles R.
2002
A Gershgorin-type lower bound for the smallest singular value. Zbl 0723.15013
Johnson, Charles R.
1989
Lower bounds for the spread of a matrix. Zbl 0578.15013
Johnson, Charles R.; Kumar, Ravinder; Wolkowicz, Henry
1985
On the possible multiplicities of the eigenvalues of a Hermitian matrix whose graph is a tree. Zbl 1001.15004
Johnson, Charles R.; Leal Duarte, António
2002
The range of $$A^{-1} A^*$$ in GL(n,C). Zbl 0292.15007
DePrima, C. R.; Johnson, C. R.
1974
The singular values of a Hadamard product: a basic inequality. Zbl 0633.15011
Ando, T.; Horn, Roger A.; Johnson, Charles R.
1987
Inertia possibilities for completions of partial Hermitian matrices. Zbl 0548.15020
Johnson, Charles R.; Rodman, Leiba
1984
On the minimum rank among positive semidefinite matrices with a given graph. Zbl 1226.05151
Booth, Matthew; Hackney, Philip; Harris, Benjamin; Johnson, Charles R.; Lay, Margaret; Mitchell, Lon H.; Narayan, Sivaram K.; Pascoe, Amanda; Steinmetz, Kelly; Sutton, Brian D.; Wang, Wendy
2008
A note on cospectral graphs. Zbl 0431.05021
Johnson, Charles R.; Newman, Morris
1980
Determinantal formulae for matrix completions associated with chordal graphs. Zbl 0681.15003
Barrett, Wayne W.; Johnson, Charles R.; Lundquist, Michael
1989
Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: The case of generalized stars and double generalized stars. Zbl 1035.15010
Johnson, Charles R.; Leal Duarte, António; Saiago, Carlos M.
2003
The real positive definite completion problem for a simple cycle. Zbl 0786.15027
Barrett, Wayne; Johnson, Charles R.; Tarazaga, Pablo
1993
The Euclidean distance matrix completion problem. Zbl 0823.15012
Bakonyi, Mihály; Johnson, Charles R.
1995
Convex sets of nonsingular and $$P$$-matrices. Zbl 0824.15021
Johnson, Charles R.; Tsatsomeros, Michael J.
1995
On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph. Zbl 1022.15030
Johnson, Charles R.; Duarte, António Leal; Saiago, Carlos M.; Sutton, Brian D.; Witt, Andrew J.
2003
Further lower bounds for the smallest singular value. Zbl 0891.15013
Johnson, Charles R.; Szulc, Tomasz
1998
Normality and the numerical range. Zbl 0337.15019
Johnson, Charles R.
1976
The real positive definite completion problem: Cycle completability. Zbl 0857.05068
Barrett, Wayne W.; Johnson, Charles R.; Loewy, Raphael
1996
The completion problem for $$M$$-matrices and inverse $$M$$-matrices. Zbl 0979.15009
Johnson, Charles R.; Smith, Ronald L.
1996
Connections between the real positive semidefinite and distance matrix completion problems. Zbl 0827.15032
Johnson, Charles R.; Tarazaga, Pablo
1995
On matrices with Perron–Frobenius properties and some negative entries. Zbl 1078.15018
Johnson, Charles R.; Tarazaga, Pablo
2004
Sign patterns that require real, nonreal or pure imaginary eigenvalues. Zbl 0764.05015
Eschenbach, Carolyn A.; Johnson, Charles R.
1991
Sign patterns of inverse-positive matrices. Zbl 0404.15007
Johnson, Charles R.; Leighton, Frank Thomson; Robinson, Herbert A.
1979
Linear maps on Hermitian matrices: The stabilizer of an inertia class. II. Zbl 0593.15021
Johnson, Charles R.; Pierce, Stephen
1986
Semipositivity of matrices. Zbl 0815.15018
Johnson, Charles R.; Kerr, M. Kathleen; Stanford, David P.
1994
A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix. Zbl 0597.15016
Fiedler, Miroslav; Johnson, Charles R.; Markham, Thomas L.; Neumann, Michael
1985
Spanning-tree extensions of the Hadamard-Fischer inequalities. Zbl 0619.05021
Johnson, Charles R.; Barrett, Wayne W.
1985
Completion of partial matrices to contractions. Zbl 0626.47015
Johnson, Charles R.; Rodman, Leiba
1986
Positive definite matrices. Zbl 0261.15012
Johnson, C. R.
1970
The combinatorially symmetric $$P$$-matrix completion problem. Zbl 0889.15007
Johnson, Charles R.; Kroschel, Brenda K.
1996
Hadamard and conventional submultiplicativity for unitarily invariant norms on matrices. Zbl 0605.15017
Horn, Roger A.; Johnson, Charles R.
1987
Mathematical aspects of the relative gain array $$(A\circ A^{-T})$$. Zbl 0607.15013
Johnson, Charles R.; Shapiro, Helene M.
1986
Sub-direct sums and positivity classes of matrices. Zbl 0973.15013
Fallat, Shaun M.; Johnson, Charles R.
1999
Determinantal formulae for matrices with sparse inverses. Zbl 0523.15008
Barrett, Wayne W.; Johnson, Charles R.
1984
A generalization of Sylvester’s law of inertia. Zbl 0993.15011
2001
A semi-definite Lyapunov theorem and the characterization of tridiagonal D-stable matrices. Zbl 0541.15008
Carlson, David; Datta, B. N.; Johnson, Charles R.
1982
On the minimum semidefinite rank of a simple graph. Zbl 1223.05170
Booth, Matthew; Hackney, Philip; Harris, Benjamin; Johnson, Charles R.; Lay, Margaret; Lenker, Terry D.; Mitchell, Lon H.; Narayan, Sivaram K.; Pascoe, Amanda; Sutton, Brian D.
2011
The potentially stable tree sign patterns for dimensions less than five. Zbl 0723.05047
Johnson, Charles R.; Summers, Tracy A.
1989
Eigenvalues of words in two positive definite letters. Zbl 1007.68139
Johnson, Charles R.; Hillar, Christopher J.
2002
Nested sequences of principal minors and potential stability. Zbl 0880.15025
Johnson, Charles R.; Maybee, John S.; Olesky, D. D.; van den Driessche, P.
1997
Some sign patterns that preclude matrix stability. Zbl 0676.15004
Jeffries, Clark; Johnson, Charles R.
1988
Uniqueness of matrix square roots and an application. Zbl 0976.15009
Johnson, Charles R.; Okubo, Kazuyoshi; Reams, Robert
2001
Monotonicity properties of norms. Zbl 0717.15015
Johnson, Charles R.; Nylen, Peter
1991
On the reduction of pairs of Hermitian or symmetric matrices to diagonal form by congruence. Zbl 0593.15005
Yoo Pyo Hong; Horn, Roger A.; Johnson, Charles R.
1986
Second, third, and fourth order D-stability. Zbl 0283.15005
Johnson, Charles R.
1974
The graphs for which the maximum multiplicity of an eigenvalue is two. Zbl 1225.05167
Johnson, Charles R.; Loewy, Raphael; Smith, Paul Anthony
2009
Matrices with chordal inverse zero-patterns. Zbl 0787.15007
Johnson, Charles R.; Lundquist, Michael
1993
Spectral theory of copositive matrices. Zbl 1064.15007
Johnson, Charles R.; Reams, Robert
2005
Linear transformations on $$M_ n({\mathbb{R}})$$ that preserve the Ky Fan k- norm and a remarkable special case when $$(n,k)=(4,2)$$. Zbl 0658.15029
Johnson, Charles R.; Laffey, Thomas; Li, Chi-Kwong
1988
Sign patterns of inverse nonnegative matrices. Zbl 0519.15008
Johnson, Charles R.
1983
Convex sets of Hermitian matrices with constant inertia. Zbl 0577.15007
Johnson, Charles R.; Rodman, Leiba
1985
Sign patterns that require repeated eigenvalues. Zbl 0795.15008
Eschenbach, Carolyn A.; Johnson, Charles R.
1993
The relationship between $$AB$$ and $$BA$$. Zbl 0865.15010
Johnson, Charles R.; Schreiner, Erik A.
1996
A combinatorial converse to the Perron-Frobenius theorem. Zbl 0739.15004
Eschenbach, Carolyn A.; Johnson, Charles R.
1990
Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix. Zbl 0999.15005
Johnson, Charles R.; Saiago, Carlos M.
2002
Eigenvalue inequalities for principal submatrices. Zbl 0458.15013
Johnson, Charles R.; Robinson, Herbert A.
1981
The no long odd cycle theorem for completely positive matrices. Zbl 0838.15011
Drew, John H.; Johnson, Charles R.
1996
Spectra of matrices with P-matrix powers. Zbl 0612.15013
Hershkowitz, Daniel; Johnson, Charles R.
1986
On the effect of the perturbation of a nonnegative matrix on its Perron eigenvector. Zbl 0501.15010
Elsner, L.; Johnson, C. R.; Neumann, M.
1982
Perron spectratopes and the real nonnegative inverse eigenvalue problem. Zbl 1329.15028
Johnson, Charles R.; Paparella, Pietro
2016
Inverse $$M$$-matrices. II. Zbl 1218.15015
Johnson, Charles R.; Smith, Ronald L.
2011
$$P$$-matrix completions under weak symmetry assumptions. Zbl 0963.15021
Fallat, Shaun M.; Johnson, Charles R.; Torregrosa, Juan R.; Urbano, Ana M.
2000
Notes on inverse M-matrices. Zbl 0618.15012
Fiedler, M.; Johnson, Charles R.; Markham, T. L.
1987
Some outstanding problems in the theory of matrices. Zbl 0494.15002
Johnson, Charles R.
1982
Olga, matrix theory and the Taussky unification problem. Zbl 0946.15001
Johnson, Charles R.; Fallat, Shaun
1998
Total positivity of sums, Hadamard products and Hadamard powers: results and counterexamples. Zbl 1359.15027
Fallat, Shaun; Johnson, Charles R.; Sokal, Alan D.
2017
Constructing copositive matrices from interior matrices. Zbl 1143.15023
Johnson, Charles R.; Reams, Robert
2008
Matrix analysis. Transl. from the English by Kh. D. Ikramov, A. V. Knyazev and E. E. Tyrtyshnikov. Transl. ed. and with a foreword by Ikramov. (Матричный анализ.) Zbl 0734.15002
Horn, Roger A.; Johnson, Charles R.
1989
The general totally positive matrix completion problem with few unspecified entries. Zbl 0941.15009
Fallat, Shaun M.; Johnson, Charles R.; Smith, Ronald L.
2000
Completing a block diagonal matrix with a partially prescribed inverse. Zbl 0831.15010
Barrett, Wayne W.; Lundquist, Michael E.; Johnson, Charles R.; Woerdeman, Hugo J.
1995
An inclusion region for the field of values of a doubly stochastic matrix based on its graph. Zbl 0384.15006
Johnson, Charles R.
1978
A surprising determinantal inequality for real matrices. Zbl 0407.15009
Johnson, Charles R.; Newman, Morris
1980
The copositive completion problem. Zbl 1098.15010
Hogben, Leslie; Johnson, Charles R.; Reams, Robert
2005
A simple estimate of the condition number of a linear system. Zbl 1291.15022
Guggenheimer, Heinrich W.; Edelman, Alan S.; Johnson, Charles R.
1995
Inherited matrix entries: LU factorizations. Zbl 0667.65027
Johnson, Charles R.; Olesky, D. D.; van den Driessche, P.
1989
The Hadamard core of the totally nonnegative matrices. Zbl 0989.15009
Crans, Alissa S.; Fallat, Shaun M.; Johnson, Charles R.
2001
Minimum rank completions. Zbl 0775.15001
Johnson, Charles R.; Whitney, Glen T.
1991
Combinatorial matrix analysis: An overview. Zbl 0652.15001
Johnson, Charles R.
1988
Complementary bases in symplectic matrices and a proof that their determinant is one. Zbl 1112.15002
Dopico, Froilán M.; Johnson, Charles R.
2006
Linear maps on Hermitian matrices: the stabilizer of an inertia class. Zbl 0577.15008
Johnson, Charles R.; Pierce, Stephen
1985
Linear transformations that preserve certain positivity classes of matrices. Zbl 0583.15013
Berman, Abraham; Hershkowitz, Daniel; Johnson, Charles R.
1985
The structure of matrices with a maximum multiplicity eigenvalue. Zbl 1143.15005
Johnson, Charles R.; Leal Duarte, António; Saiago, Carlos M.
2008
Nonnegative realizability with Jordan structure. Zbl 07191023
Johnson, Charles R.; Julio, Ana I.; Soto, Ricardo L.
2020
The proportion of trees that are linear. Zbl 1445.05051
Wakhare, Tanay; Wityk, Eric; Johnson, Charles R.
2020
Matrix positivity. Zbl 1469.15002
Johnson, Charles R.; Smith, Ronald L.; Tsatsomeros, Michael J.
2020
Target control and source estimation metrics for dynamical networks. Zbl 1415.93055
Vosughi, Amirkhosro; Johnson, Charles; Xue, Mengran; Roy, Sandip; Warnick, Sean
2019
The change in multiplicity of an eigenvalue due to adding or removing edges. Zbl 1403.15007
Johnson, Charles R.; Saiago, Carlos M.; Toyonaga, Kenji
2019
Eigenvalues, multiplicities and graphs. Zbl 1433.05002
Johnson, Charles R.; Saiago, Carlos M.
2018
Universal realizability of spectra with two positive eigenvalues. Zbl 1391.15037
Collao, Macarena; Johnson, Charles R.; Soto, Ricardo L.
2018
Geometric Parter-Wiener, etc. theory. Zbl 1376.15030
Johnson, Charles R.; Saiago, Carlos M.
2018
Classification of vertices and edges with respect to the geometric multiplicity of an eigenvalue in a matrix, with a given graph, over a field. Zbl 1406.15014
Johnson, Charles R.; Saiago, Carlos M.; Toyonaga, Kenji
2018
The NIEP. Zbl 1427.15001
Johnson, Charles R.; Marijuán, Carlos; Paparella, Pietro; Pisonero, Miriam
2018
The minimum number of eigenvalues of multiplicity one in a diagonalizable matrix, over a field, whose graph is a tree. Zbl 1403.15006
Johnson, Charles R.; Leal-Duarte, António; Saiago, Carlos M.
2018
Multiplicity lists for symmetric matrices whose graphs have few missing edges. Zbl 1380.15009
Johnson, Charles R.; Zhang, Yulin
2018
Total positivity of sums, Hadamard products and Hadamard powers: results and counterexamples. Zbl 1359.15027
Fallat, Shaun; Johnson, Charles R.; Sokal, Alan D.
2017
Ruling out certain 5-spectra for the symmetric nonnegative inverse eigenvalue problem. Zbl 1353.15008
Johnson, C. R.; Marijuán, C.; Pisonero, M.
2017
The classification of edges and the change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the change in an edge value. Zbl 1360.15014
Toyonaga, Kenji; Johnson, Charles R.
2017
Symmetric nonnegative realizability via partitioned majorization. Zbl 1375.15015
Johnson, C. R.; Marijuán, C.; Pisonero, M.
2017
A matricial view of the Karpelevič theorem. Zbl 1359.15029
Johnson, Charles R.; Paparella, Pietro
2017
Changes in vertex status and the fundamental decomposition of a tree relative to a multiple (parter) eigenvalue. Zbl 1372.05172
Johnson, Charles R.; Leal-Duarte, António; McMichael, Paul R.
2017
On the solvability of derived matrix problems, including completions and duals. Zbl 1349.14180
Johnson, Charles R.; Leal-Duarte, António
2017
Perron spectratopes and the real nonnegative inverse eigenvalue problem. Zbl 1329.15028
Johnson, Charles R.; Paparella, Pietro
2016
Inverse spectral problems for collections of leading principal submatrices of tridiagonal matrices. Zbl 1325.15032
Higgins, Vijay; Johnson, Charles
2016
Diameter minimal trees. Zbl 1338.05160
Johnson, Charles R.; Saiago, Carlos M.
2016
Linear preservers of semi-positive matrices. Zbl 1388.15026
Dorsey, Jonathan; Gannon, Tom; Jacobson, Nathaniel; Johnson, Charles R.; Turnansky, Morrison
2016
New results about semi-positive matrices. Zbl 1413.15021
Dorsey, Jonathan; Gannon, Tom; Johnson, Charles R.; Turnansky, Morrison
2016
Ranks of permutative matrices. Zbl 1338.05030
Hu, Xiaonan; Johnson, Charles R.; Davis, Caroline E.; Zhang, Yimeng
2016
Questions, conjectures, and data about multiplicity lists for trees. Zbl 1350.05092
Buckley, Shannon P.; Corliss, Joseph G.; Johnson, Charles R.; Araúz Lombardía, Cristina; Saiago, Carlos M.
2016
Sufficient conditions to be exceptional. Zbl 1338.15025
Johnson, Charles R.; Reams, Robert B.
2016
Normal matrices subordinate to a tree and flat portions of the field of values. Zbl 1343.05093
Johnson, Charles R.; Spitkovsky, Ilya M.; Stevanovic, Mirjana; Turnansky, Morrison
2016
The number of interlacing equalities resulting from removal of a vertex from a tree. Zbl 1320.15005
Farber, Miriam; Johnson, Charles; Zhang, Leon
2015
The structure of Schur complements in hollow, symmetric nonnegative matrices with two nonpositive eigenvalues. Zbl 1369.15021
Farber, Miriam; Johnson, Charles R.
2015
Ordered multiplicity lists for eigenvalues of symmetric matrices whose graph is a linear tree. Zbl 1298.05068
Johnson, Charles R.; Li, Andrew A.; Walker, Andrew J.
2014
Undirected graphs of Hermitian matrices that admit only two distinct eigenvalues. Zbl 1295.05141
Chen, Zhao; Grimm, Matthew; McMichael, Paul; Johnson, Charles R.
2014
Equal entries in totally positive matrices. Zbl 1291.15077
Farber, Miriam; Faulk, Mitchell; Johnson, Charles R.; Marzion, Evan
2014
Complete solution to the $$TP_{2}$$ completion problem. Zbl 1307.15039
Johnson, C. R.; Nasserasr, S.
2014
On the similarity classes among products of $$m$$ nonsingular matrices in various orders. Zbl 1302.15015
2014
Submatrix monotonicity of the Perron root. II. Zbl 1294.15009
Furtado, Susana; Johnson, C. R.; Marijuán, C.; Pisonero, M.
2014
TP$$_k$$ completions of partial matrices with one unspecified entry. Zbl 1327.15059
Akin, V.; Johnson, C. R.; Nasserasr, S.
2014
Exact results for perturbation to total positivity and to total nonsingularity. Zbl 1327.15067
Farber, Miriam; Faulk, Mitchell; Johnson, Charles R.; Marzion, Evan
2014
Matrix analysis. 2nd ed. Zbl 1267.15001
Horn, Roger A.; Johnson, Charles R.
2013
Continuity properties of vectors realizing points in the classical field of values. Zbl 1290.15012
Corey, Dan; Johnson, Charles R.; Kirk, Ryan; Lins, Brian; Spitkovsky, Ilya
2013
The implicit construction of multiplicity lists for classes of trees and verification of some conjectures. Zbl 1258.05070
Johnson, Charles R.; Nuckols, Jonathan; Spicer, Calum
2013
Nonpositive eigenvalues of hollow, symmetric, nonnegative matrices. Zbl 1282.15016
Charles, Zachary B.; Farber, Miriam; Johnson, Charles R.; Kennedy-Shaffer, Lee
2013
Asymmetric TP and TN completion problems. Zbl 1261.15035
Johnson, Charles R.; Wei, Zhen
2013
The product field of values. Zbl 1272.15015
Corey, Daniel; Johnson, Charles R.; Kirk, Ryan; Lins, Brian; Spitkovsky, Ilya
2013
Nonpositive eigenvalues of the adjacency matrix and lower bounds for Laplacian eigenvalues. Zbl 1279.05046
Charles, Zachary B.; Farber, Miriam; Johnson, Charles R.; Kennedy-Shaffer, Lee
2013
Inequalities for linear combinations of monomials in p-Newton sequences. Zbl 1305.15022
Johnson, C. R.; Marijuán, C.; Pisonero, M.
2013
When the positivity of the leading principal minors implies the positivity of all principal minors of a matrix. Zbl 1283.15107
Johnson, Charles R.; Narayan, Sivaram K.
2013
The distribution of eigenvalues of doubly cyclic $$Z^+$$-matrices. Zbl 1283.15059
Johnson, Charles R.; Price, Zachary; Spitkovsky, Ilya M.
2013
Eigenvalue pairing in the response matrix for a class of network models with circular symmetry. Zbl 1295.05143
Farber, Miriam; Johnson, Charles R.; Zhen, Wei
2013
The change in eigenvalue multiplicity associated with perturbation of a diagonal entry. Zbl 1247.15007
Johnson, Charles R.; Leal-Duarte, António; Saiago, Carlos M.
2012
Critical exponents: old and new. Zbl 1251.15011
Johnson, Charles R.; Walch, Olivia
2012
Submatrix monotonicity of the Perron root. Zbl 1255.15040
Johnson, C. R.; Marijuán, C.; Pisonero, M.
2012
Minimizing the least eigenvalue of graphs with fixed order and size. Zbl 1245.05086
Johnson, Charles R.; Sawikowska, Aneta
2012
Optimal Gersgorin-style estimation of the singular value. Zbl 1250.65054
Johnson, Ch. R.; Pena, J. M.; Szulc, T.
2012
Totally positive shapes and $$TP_{k}$$-completable patterns. Zbl 1242.15023
Hoff, D.; Johnson, C. R.; Nasserasr, S.
2012
Totally nonnegative matrices. Zbl 1390.15001
Fallat, Shaun M.; Johnson, Charles R.
2011
On the minimum semidefinite rank of a simple graph. Zbl 1223.05170
Booth, Matthew; Hackney, Philip; Harris, Benjamin; Johnson, Charles R.; Lay, Margaret; Lenker, Terry D.; Mitchell, Lon H.; Narayan, Sivaram K.; Pascoe, Amanda; Sutton, Brian D.
2011
Inverse $$M$$-matrices. II. Zbl 1218.15015
Johnson, Charles R.; Smith, Ronald L.
2011
The change in multiplicity of an eigenvalue of a Hermitian matrix associated with the removal of an edge from its graph. Zbl 1225.05168
Johnson, Charles R.; McMichael, Paul R.
2011
The critical exponent for continuous conventional powers of doubly nonnegative matrices. Zbl 1221.15046
Johnson, Charles R.; Lins, Brian; Walch, Olivia
2011
The ratio field of values. Zbl 1209.15024
Einstein, Eduard; Johnson, Charles R.; Lins, Brian; Spitkovsky, Ilya
2011
Equilibrants, semipositive matrices, calculation and scaling. Zbl 1211.15045
Johnson, Charles R.; Tong, Zheng
2011
Monomial inequalities for Newton coefficients and determinantal inequalities for $$p$$-Newton matrices. Zbl 1250.15025
Johnson, C. R.; Marijuán, C.; Pisonero, M.; Walch, O.
2011
Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree. Zbl 1225.05166
Johnson, Charles R.; Jordan-Squire, Christopher; Sher, David A.
2010
On the possible ranks among matrices with a given pattern. Zbl 1210.15002
Johnson, Charles R.; Zhang, Yulin
2010
Order invariant spectral properties for several matrices. Zbl 1187.15011
2010
TP$$_2$$ = Bruhat. Zbl 1225.05009
Johnson, C. R.; Nasserasr, S.
2010
The Jordan form problem for $$C = AB$$: the balanced, diagonalizable case. Zbl 1213.15010
Johnson, Charles R.; Zhang, YuLin
2010
Gangster operators and invincibility of positive semidefinite matrices. Zbl 1216.15023
Ferguson, Timothy; Johnson, Charles
2010
The graphs for which the maximum multiplicity of an eigenvalue is two. Zbl 1225.05167
Johnson, Charles R.; Loewy, Raphael; Smith, Paul Anthony
2009
Matrices and spectra satisfying the Newton inequalities. Zbl 1189.15009
Johnson, C. R.; Marijuán, C.; Pisonero, M.
2009
Scaling of symmetric matrices by positive diagonal congruence. Zbl 1166.15011
Johnson, Charles R.; Reams, Robert
2009
Parametrization of the matrix symplectic group and applications. Zbl 1193.15011
Dopico, Froilán M.; Johnson, Charles R.
2009
Implicit construction of multiple eigenvalues for trees. Zbl 1176.15011
Johnson, Charles R.; Sutton, Brian D.; Witt, Andrew J.
2009
General resolution of a convergence question of L. Krukier. Zbl 1224.15044
Johnson, Charles; Krukier, Lev
2009
Solution theory for complete bilinear systems of equations. Zbl 1224.15047
Johnson, Charles R.; Link, Joshua A.
2009
Totally positive completions for monotonically labeled block clique graphs. Zbl 1171.05360
Johnson, Charles R.; Negron, Cris
2009
Variation in Jordan structure under congruence: the nonsingular case. Zbl 1171.15009
2009
Matrices totally positive relative to a tree. Zbl 1171.15021
Johnson, Charles R.; Costas-Santos, Roberto S.; Tadchiev, Boris
2009
On the minimum rank among positive semidefinite matrices with a given graph. Zbl 1226.05151
Booth, Matthew; Hackney, Philip; Harris, Benjamin; Johnson, Charles R.; Lay, Margaret; Mitchell, Lon H.; Narayan, Sivaram K.; Pascoe, Amanda; Steinmetz, Kelly; Sutton, Brian D.; Wang, Wendy
2008
Constructing copositive matrices from interior matrices. Zbl 1143.15023
Johnson, Charles R.; Reams, Robert
2008
The structure of matrices with a maximum multiplicity eigenvalue. Zbl 1143.15005
Johnson, Charles R.; Leal Duarte, António; Saiago, Carlos M.
2008
Branch duplication for the construction of multiple eigenvalues in an Hermitian matrix whose graph is a tree. Zbl 1149.15007
Johnson, Charles R.; Saiago, Carlos M.
2008
Path product matrices and eventually inverse $$M$$-matrices. Zbl 1141.15020
Johnson, Charles R.; Smith, Ronald L.
2008
The extent to which triangular sub-patterns explain minimum rank. Zbl 1152.05312
Johnson, Charles R.; Link, Joshua A.
2008
Schur-type stability properties and complex diagonal scaling. Zbl 1155.15005
Johnson, Charles R.; Lenker, Terry D.; Narayan, Sivaram K.
2008
Matrices with orthogonal groups admitting only determinant one. Zbl 1136.15008
Coakley, Edward S.; Dopico, Froilán M.; Johnson, Charles R.
2008
Hadamard powers and totally positive matrices. Zbl 1123.15014
Fallat, Shaun M.; Johnson, Charles R.
2007
Unitarily achievable zero patterns and traces of words in $$A$$ and $$A$$. Zbl 1122.15014
Đoković, Dragomir Ž.; Johnson, Charles R.
2007
Positive, path product, and inverse $$M$$-matrices. Zbl 1124.15018
Johnson, Charles R.; Smith, Ronald L.
2007
Matrices that preserve vectors of fixed sign variation. Zbl 1132.15003
Johnson, C. R.; Peña, J. M.
2007
Hadamard duals retractability and Oppenheim’s inequality. Zbl 1137.15009
Fallat, Shaun M.; Johnson, Charles R.
2007
Products of $$M$$-matrices and nested sequences of principal minors. Zbl 1153.15026
Grundy, D. A.; Johnson, C. R.; Olesky, D. D.; van den Driessche, P.
2007
Minimum deviation, quasi-LU factorization of nonsingular matrices. Zbl 1133.15013
Bueno, M. I.; Johnson, C. R.
2007
Congruence of Hermitian matrices by Hermitian matrices. Zbl 1126.15011
Bueno, M. I.; Furtado, S.; Johnson, C. R.
2007
Complementary bases in symplectic matrices and a proof that their determinant is one. Zbl 1112.15002
Dopico, Froilán M.; Johnson, Charles R.
2006
Compressions of totally positive matrices. Zbl 1112.15024
Fallat, Shaun M.; Herman, Allen; Gekhtman, Michael I.; Johnson, Charles R.
2006
Converse to the Parter–Wiener theorem: the case of non-trees. Zbl 1114.05061
Johnson, C. R.; Duarte, António Leal
2006
Multiple LU factorizations of a singular matrix. Zbl 1106.15009
Dopico, Froilán M.; Johnson, Charles R.; Molera, Juan M.
2006
Eigenvalues, multiplicities and graphs. Zbl 1114.15007
Johnson, Charles R.; Duarte, António Leal; Saiago, Carlos M.; Sher, David
2006
...and 268 more Documents
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#### Cited by 9,694 Authors

 267 Johnson, Charles Royal 100 Li, Chi-Kwong 67 Ikramov, Saidkhakim Dododshanovich 66 van den Driessche, Pauline 47 Huang, Ting-Zhu 44 Olesky, D. Dale 41 Fallat, Shaun M. 37 Horn, Roger Alan 35 Tsatsomeros, Michael J. 34 Cao, Jinde 31 Hogben, Leslie 31 Peña, Juan Manuel 29 Rodman, Leiba X. 29 Spitkovsky, Ilya Matvey 28 Neumann, Michael 28 Wei, Yimin 27 Loewy, Raphael 26 Soto, Ricardo Lorenzo 26 Xu, Daoyi 25 Sergeichuk, Vladimir Vasil’evich 24 Chen, Guanrong 24 Gau, Hwa-Long 24 Hall, Frank J. 24 Li, Zhongshan 24 Liu, Jianzhou 24 Shader, Bryan L. 24 Tam, Tin-Yau 24 Zhang, Fuzhen 23 Kirkland, Steve J. 23 Psarrakos, Panayiotis J. 23 Wu, Peiyuan 22 Merino, Dennis I. 22 Rojo, Oscar L. 22 Tian, Yongge 21 Bebiano, Natália Isabel Quadros 21 Chien, Mao-Ting 21 Elsner, Ludwig F. 20 Dopico, Froilán M. 20 Furtado, Susana 20 Sze, Nung-Sing 19 Bapat, Ravindra Bhalchandra 19 Barrett, Wayne W. 19 da Fonseca, Carlos Martins 19 Gao, Yubin 19 Hershkowitz, Daniel 19 Marijuán, Carlos 19 Nakazato, Hiroshi 19 Narayan, Sivaram K. 19 Šmigoc, Helena 19 Tsing, Nam-Kiu 18 Berman, Abraham S. 18 Kittaneh, Fuad 18 Mcdonald, Judith Joanne 18 Paras, Agnes T. 18 Pisonero, Miriam 18 Smith, Ronald L. 17 Benzi, Michele 17 Fan, Yizheng 17 Laffey, Thomas J. 17 Shorten, Robert N. 17 Wolkowicz, Henry 16 Cheng, Cheman 16 da Providência Santarém e Costa, João 16 Drury, Stephen William 16 Higham, Nicholas J. 16 Lewkowicz, Izchak 16 Lu, Jianquan 16 Mehrmann, Volker 16 Merikoski, Jorma Kaarlo 16 Poon, Yiu-Tung 16 Saiago, Carlos M. 16 Simoncini, Valeria 15 Kolotilina, Lily Yu. 15 Li, Wen 15 Lin, Minghua 15 Reichel, Lothar 15 Shao, Yanling 15 Sivakumar, Koratti Chengalrayan 15 Tarazaga, Pablo A. 15 Uhlig, Frank 15 Urbano, Ana María 14 de Terán, Fernando 14 Eschenbach, Carolyn A. 14 Garcia, Stephan Ramon 14 Lim, Yongdo 14 Mason, Oliver 14 Mehl, Christian 14 Nylen, Peter M. 14 Paparella, Pietro 14 Torregrosa Sanchez, Juan Ramón 14 Vander Meulen, Kevin N. 14 Wu, Aiguo 14 Xu, Jianhong 14 Zhang, Xiaodong 13 Akbari, Saieed 13 Benner, Peter 13 Bhatia, Rajendra 13 Faßbender, Heike 13 Fiedler, Miroslav 13 Gowda, Muddappa Seetharama ...and 9,594 more Authors
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#### Cited in 699 Serials

 2,028 Linear Algebra and its Applications 342 Linear and Multilinear Algebra 222 Automatica 196 Applied Mathematics and Computation 156 Journal of Computational and Applied Mathematics 121 Journal of Mathematical Analysis and Applications 100 SIAM Journal on Matrix Analysis and Applications 99 Journal of the Franklin Institute 97 Systems & Control Letters 86 International Journal of Control 71 Computers & Mathematics with Applications 64 Proceedings of the American Mathematical Society 64 Mathematical Programming. Series A. Series B 60 Journal of Mathematical Physics 59 ELA. The Electronic Journal of Linear Algebra 55 Discrete Mathematics 54 Journal of Mathematical Sciences (New York) 54 Numerical Linear Algebra with Applications 51 Journal of Optimization Theory and Applications 51 Special Matrices 50 Discrete Applied Mathematics 47 The Annals of Statistics 46 Journal of Multivariate Analysis 45 Journal of Econometrics 45 Numerical Algorithms 44 International Journal of Robust and Nonlinear Control 43 Journal of Computational Physics 43 Applied Numerical Mathematics 41 Applied Mathematics Letters 40 BIT 39 Numerische Mathematik 38 Mathematics of Computation 38 Journal of Inequalities and Applications 35 Czechoslovak Mathematical Journal 35 SIAM Journal on Scientific Computing 35 Mathematical Problems in Engineering 34 Statistics & Probability Letters 33 Abstract and Applied Analysis 31 Physics Letters. A 31 Applied and Computational Harmonic Analysis 30 Journal of Functional Analysis 30 European Journal of Operational Research 29 SIAM Journal on Optimization 29 Computational Optimization and Applications 28 Transactions of the American Mathematical Society 28 Automation and Remote Control 28 Nonlinear Dynamics 27 Integral Equations and Operator Theory 27 Journal of Theoretical Probability 24 Chaos, Solitons and Fractals 24 Journal of Differential Equations 24 Journal of Statistical Planning and Inference 24 Journal of Scientific Computing 23 Neural Networks 23 Journal of Global Optimization 23 International Journal of Computer Mathematics 23 Journal of Applied Mathematics 23 Journal of Applied Mathematics and Computing 22 Communications in Mathematical Physics 22 Journal of Statistical Physics 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 22 Mathematical and Computer Modelling 22 Quantum Information Processing 22 Advances in Difference Equations 22 International Journal of Systems Science. Principles and Applications of Systems and Integration 21 Computer Methods in Applied Mechanics and Engineering 21 Optimization Methods & Software 21 Chaos 20 Signal Processing 20 Doklady Mathematics 20 Electronic Journal of Statistics 19 International Journal of Systems Science 19 Mathematical Notes 19 The Annals of Probability 19 Journal of Approximation Theory 19 The Annals of Applied Probability 19 Positivity 18 Journal of Mathematical Biology 18 Fuzzy Sets and Systems 18 Journal of Mathematical Economics 18 SIAM Journal on Algebraic and Discrete Methods 18 Physica D 18 Computational Statistics and Data Analysis 18 Differential Equations 18 Journal of Systems Science and Complexity 17 Rocky Mountain Journal of Mathematics 17 Journal of Algebra 17 SIAM Journal on Control and Optimization 17 Acta Mathematicae Applicatae Sinica. English Series 17 Probability Theory and Related Fields 17 Complexity 17 Bernoulli 17 Acta Mathematica Sinica. English Series 17 Journal of Machine Learning Research (JMLR) 16 Mathematical Biosciences 16 Theoretical Computer Science 16 Applied Mathematical Modelling 16 Communications in Statistics. Theory and Methods 16 Stochastic Processes and their Applications 16 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering ...and 599 more Serials
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#### Cited in 61 Fields

 3,612 Linear and multilinear algebra; matrix theory (15-XX) 1,501 Numerical analysis (65-XX) 1,103 Systems theory; control (93-XX) 1,077 Combinatorics (05-XX) 649 Operations research, mathematical programming (90-XX) 533 Operator theory (47-XX) 533 Probability theory and stochastic processes (60-XX) 524 Statistics (62-XX) 460 Computer science (68-XX) 436 Ordinary differential equations (34-XX) 303 Biology and other natural sciences (92-XX) 269 Partial differential equations (35-XX) 269 Information and communication theory, circuits (94-XX) 244 Quantum theory (81-XX) 240 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 210 Dynamical systems and ergodic theory (37-XX) 155 Harmonic analysis on Euclidean spaces (42-XX) 148 Functional analysis (46-XX) 146 Calculus of variations and optimal control; optimization (49-XX) 143 Number theory (11-XX) 104 Real functions (26-XX) 102 Statistical mechanics, structure of matter (82-XX) 96 Difference and functional equations (39-XX) 93 Functions of a complex variable (30-XX) 91 Convex and discrete geometry (52-XX) 83 Special functions (33-XX) 83 Fluid mechanics (76-XX) 79 Approximations and expansions (41-XX) 76 Mechanics of deformable solids (74-XX) 70 Group theory and generalizations (20-XX) 63 Differential geometry (53-XX) 63 Mechanics of particles and systems (70-XX) 60 Algebraic geometry (14-XX) 54 Associative rings and algebras (16-XX) 47 Commutative algebra (13-XX) 40 Global analysis, analysis on manifolds (58-XX) 39 Nonassociative rings and algebras (17-XX) 38 Topological groups, Lie groups (22-XX) 37 Field theory and polynomials (12-XX) 37 Geometry (51-XX) 33 Abstract harmonic analysis (43-XX) 32 Several complex variables and analytic spaces (32-XX) 30 Integral transforms, operational calculus (44-XX) 29 Integral equations (45-XX) 25 Measure and integration (28-XX) 24 Optics, electromagnetic theory (78-XX) 23 Order, lattices, ordered algebraic structures (06-XX) 20 Manifolds and cell complexes (57-XX) 17 General topology (54-XX) 17 Geophysics (86-XX) 16 Relativity and gravitational theory (83-XX) 15 Potential theory (31-XX) 14 General and overarching topics; collections (00-XX) 12 Mathematical logic and foundations (03-XX) 11 Classical thermodynamics, heat transfer (80-XX) 7 Category theory; homological algebra (18-XX) 7 Mathematics education (97-XX) 5 Algebraic topology (55-XX) 4 History and biography (01-XX) 4 Sequences, series, summability (40-XX) 2 General algebraic systems (08-XX)

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